We construct Super-Eddington Slim discs models around both stellar and supermassive black holes by allowing the formation of a porous layer with a reduced effective opacity. Unlike the standard scenario in which the discs become thick, super-Eddington discs remain slim. In addition, they accelerate a significant wind with a ‘thick disc’ geometry. We show that above about 1.5 times the standard critical mass accretion rate (needed to release the Eddington luminosity), the net luminosity released is above Eddington. At above about five times the standard critical rate, the central BH accretes more than the Eddington accretion rate. Above about , the disc remains slim but the wind becomes spherical, and the present model breaks down.